Problem: Solve for $x$ and $y$ using substitution. ${5x+3y = 1}$ ${y = 3x-9}$
Answer: Since $y$ has already been solved for, substitute $3x-9$ for $y$ in the first equation. ${5x + 3}{(3x-9)}{= 1}$ Simplify and solve for $x$ $5x+9x - 27 = 1$ $14x-27 = 1$ $14x-27{+27} = 1{+27}$ $14x = 28$ $\dfrac{14x}{{14}} = \dfrac{28}{{14}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = 3x-9}\thinspace$ to find $y$ ${y = 3}{(2)}{ - 9}$ $y = 6 - 9$ $y = -3$ You can also plug ${x = 2}$ into $\thinspace {5x+3y = 1}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ + 3y = 1}$ ${y = -3}$